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SIGMA 3 (2007), 075, 7 pages arXiv:0704.0495
https://doi.org/10.3842/SIGMA.2007.075
The Veldkamp Space of Two-Qubits
Metod Saniga a, Michel Planat b, Petr Pracna c and Hans Havlicek d
a) Astronomical Institute, Slovak Academy of Sciences,
SK-05960 Tatranská Lomnica, Slovak Republic
b) Institut FEMTO-ST, CNRS, Département LPMO,
32 Avenue de
l'Observatoire, F-25044 Besançon Cedex, France
c) J. Heyrovský Institute of Physical
Chemistry, Academy of Sciences of the Czech Republic, Dolejskova 3, CZ-182 23 Prague 8, Czech
Republic
d) Institut für Diskrete Mathematik und Geometrie,
Technische Universität Wien, Wiedner Hauptstraße 8-10, A-1040 Vienna, Austria
Received April 13, 2007, in final form June 18, 2007; Published online June 29, 2007
Abstract
Given a remarkable representation of the generalized
Pauli operators of two-qubits in terms of the points of the
generalized quadrangle of order two, W(2), it is shown that
specific subsets of these operators can also be associated with
the points and lines of the four-dimensional projective space over
the Galois field with two elements - the so-called Veldkamp
space of W(2). An intriguing novelty is the recognition of (uni- and tri-centric) triads
and specific pentads of the Pauli operators in addition to the ''classical'' subsets
answering to geometric hyperplanes of W(2).
Key words:
generalized quadrangles; Veldkamp spaces; Pauli operators of two-qubits.
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